Make first monk that is welcoming sit back (10)
I believe the answer is:
prioritise
'make first' is the definition.
'monk that is welcoming sit back' is the wordplay.
'monk' becomes 'prior' (I've seen this before).
'that is' becomes 'i.e.' (synonyms).
'welcoming' means one lot of letters goes inside another (in sense of 'inviting in').
'back' shows that the letters should be reversed in order.
'sit' back-to-front is 'tis'.
'ie' placed around 'tis' is 'itise'.
'prior'+'itise'='PRIORITISE'
(Other definitions for prioritise that I've seen before include "Determine relative importance of (tasks)" , "Put before all" , "treat as more important" , "Set in order of importance" .)