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43a Given back, restore centre of room perhaps (9)
Fireplace?

6d Left flyer advancing the progress of the nascent car industry (3,4)
Red flag? I think, I get the 'left flyer' definition but not the rest.

11d We hear out of place jokes at hotel straightaway.
f?r?h?i?h

43. Given back is a reversal of “if” (as in ‘on condition that’) + replace (restore)

43 "Given" for "if" sounds a bit odd, but it's reversed before "replace"
6
Early cars had to be preceded by a man carrying a red flag.
11 FORTHWITH
FORTH sounds like "fourth"; out of the first three, so not placed.
WIT - jokes
H - hotel

Thanks both.