There survive several portraits of Robert Dudley dating from around the mid-1560s, all of fairly similar type. The above portrait stands apart because of the silver brocade costume Dudley is wearing and the dog by his side. In the background is a pair of Ionic columns, possibly symbolizing the Pillars of Hercules, the famous emblem of the Emperor Charles V. Dudley’s left arm rests on a chair upholstered in red velvet, and he is holding a pair of gloves in his left hand. Both the pillars and the dog looking up to his master, and perhaps the red chair as well, are associative of Habsburg iconography, of Imperial portraits well-known at the time.
The portrait is further marked by two large coats of arms, at the upper left and right, representing the Order of of St. Michael and the Order the Garter, respectively. The Garter emblem seems to have been part of the original composition of the picture, while the other coat of arms is a later addition, after Robert Dudley became a member of the prestigious French order in early 1566. The coronet above the Garter coat of arms has been shown to be an addition as well, which clearly dates the portrait to some time before September 1564, when Dudley was made Earl of Leicester.

Thomas Howard, 4th Duke of Norfolk. Like his rival Leicester he is holding his right hand at a purse with a handkerchief.
It has been observed that the Dudley portrait is rather similar in composition to Hans Eworth’s portrait of Thomas Howard, 4th Duke of Norfolk, Robert Dudley’s most powerful enemy for the better part of the 1560s. Both men have a purse for their handkerchief hanging from their sword belt, and in Dudley’s case the piece of fine fabric is clearly visible because he is about to tuck it into the purse. The handkerchiefs may represent ‟tokens of affection“ and it has been speculated that Dudley’s might be ‟a memento of the Queen herself“.
There are further associations of this portrait with the Duke of Norfolk, handkerchiefs, and the Order of St. Michael. In March 1565, the Earl of Atholl told the English ambassador in Scotland, Thomas Randolph, a curious story about sporting life at the English court:
That early the Duke’s grace and my lord of Leicester were playing at tennis, the Queen beholding of them, and my Lord Robert being hot and sweating took the Queen’s napkin out of her hand and wiped his face, which the duke seeing said that he was too saucy, and swore that he would lay his racket upon his face; whereup rose a great trouble and the Queen offended sore with the Duke.
Within a year of this semi-legendary tennis court incident the French king wrote to Elizabeth, asking her to name two Englishmen worthy of the Order of St. Michael, the French equivalent to the Order of the Garter. Ideally, such an honour would have been bestowed on the English monarch, but as Elizabeth was a woman she could not be a knight at the same time. It was clear that King Charles IX, expecting that the Earl of Leicester might still become Elizabeth’s husband, was thinking of him as recipient, but it would have been undiplomatical to give him the honour right away. – Indeed, Elizabeth’s first reaction when she heard of the offer was to name Leicester, and only some time later did she settle on Norfolk as the second candidate. There was to be a joint investiture of the new knights, hopefully conducive to burying their dissensions. Norfolk was at first reluctant to accept but finally obeyed the queen’s wishes, whose aim it was ‟to prevent jealousy among the nobility“.

The Emperor Charles V with his dog, by Jacob Seisenegger. Some art historians believe this type of picture served as a model for the Dudley portrait.
And so on 24 January 1566 Charles IX’s special envoy, M. de Ramboilliet, led the festivities at Whitehall Palace. At ten o’clock in the morning Leicester and Norfolk, as yet having had no breakfast, ‟embraced each other and communed awhile“, before being led to the ceremony proper. The new knights were each clad in
white velvet shoes, hose, girdle and scabbard; netherstocks of white silk knit, coats with white sleeves on, of cloth of silver, edged with silver lace, and in short gowns of russet velvet, furred with leopards, the sleeves decorated with aiglettes of gold.
It all ended with a magnificent banquet, yearly to be repeated by duke and earl at considerable expenses. So, friendship was guaranteed in a way; and indeed their relations became increasingly cordial over the next years.
Sources
Hearn, Karen (ed.) (1995): Dynasties: Painting in Tudor and Jacobean England 1530–1630. Rizzoli.
Williams, Neville (1964): Thomas Howard, Fourth Duke of Norfolk. Barrie & Rockliff.