The answer, like many others, starts with "It depends."
We see such a situation in Marc's "Agent of the Imperium", in which the base staff of the prior noble in that position stayed "on the land" until a replacement arrived, but were understood to be subject to replacement at the whim of the new title holder. They had, if anything, more of a tradition to uphold than the title holder. This sort of arrangement is most likely to be the case for High/Landed nobles. The main exception would be during the creation of new titles at a world, requiring new residences and staff if the title holder is also "first of his line". Sometimes that new title just gets added to one of the higher local nobles (Baron Yori, anyone?), but if a new line is being created from the local "Emperor's Labor Pool" (retired Ceremonial nobles, or promising Honor Nobles), then they're starting from scratch.
Ceremonial and Honor nobles don't necessarily have retainers or the means to support them, but might in some circumstances. One of my favorite references here is Lord Peter Wimsey, of the British mysteries by Dorothy Sayers written a century ago. While just "the spare" in his youth, he acquired his one retainer, the loyal and multi-talented (ex-Sergeant) Bunter during World War I. Bunter had been his attache' through the war, had helped him recover from a nasty case of shell shock, and stuck with him afterwards. His brother inherited the family title, so Peter is just a Lord and not much else. Classic Honor noble in Traveller terms.