Hold tailless mammal back pretty quickly (10)
I believe the answer is:
allegretto
'pretty quickly' is the definition.
(musical direction)
'hold tailless mammal back' is the wordplay.
'hold' becomes 'allege' (both can mean to claim or maintain).
'tailless' means to remove the last letter (the tail of the word is removed).
'mammal' becomes 'otter' (otter is a kind of mammal).
'back' says the letters should be written in reverse.
'otter' back-to-front is 'retto'.
'allege' with its final letter taken off is 'alleg'.
'alleg'+'retto'='ALLEGRETTO'
(Other definitions for allegretto that I've seen before include "fairly speedily" , "quite fast" , "Moving fairly briskly (music)" , "somewhat quick" , "fairly quickly" .)