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13a Luxury purchase set back your old checking account 5 ????t
3d Customs of outspoken authors 5 r????
10a Softens up last pair of climate change deniers 9 t???e????
19a Couple short of place fit to accommodate fine horse 5 ??f??
Thanks for help

10 Tenderise, soften up (soften works better than the softens shown!). Anagram of 'deniers' and the last two letters of 'climate' (last pair).

3 RITES - sounds like WRITES, "authors as a verb

10 is it "Soften"? TENDERISE (anagram climaTE and DENIERS)

13a y ac ht

19 Fifth

F(fine) in Fit + H(horse)

Fifth is two places away from a prize