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A few posers:-
1 Down - "A little bit more time for Rex" (4) M-T- (MITE?)
8 Down - "Star keeping top undone" (4) S-N-
14 Down - "Radiographer's first, not last" (3) R-N (RUN?)
5 Down - "Sooty hearth's earliest fire" (5) S-O-T (obviously
"SHOOT" , but I can't see the first part of the clue! )

8, Sun k.

1 Mote, a little bit. 'More' swaps its R for Rex for a T for Time.
8 Sunk, undone - Sun +K(eeping).

Many thanks, Rusty and Malone - that'll help!

14 run
R(adiographer) un (not e.g. Unwell)