Drama putting off my tailor, with wages covering last of material (8,4)
I believe the answer is:
morality play
'drama' is the definition.
(morality play is a kind of drama)
'off my tailor with wages covering last of material' is the wordplay.
'off' indicates an anagram.
'with' is a charade indicator (letters next to each other).
'wages' becomes 'pay' (I've seen this before**).
'covering' is an insertion indicator.
'last of' suggests the final letters.
The final letter of 'material' is 'l'.
'pay' placed around 'l' is 'play'.
'my'+'tailor'='mytailor'
'mytailor' anagrammed gives 'morality'.
'morality'+'play'='MORALITY PLAY'
'putting' acts as a link.
(Other definitions for morality play that I've seen before include "Edifying drama" , "Improving drama" , "dramatic work providing lessons" , "Stage performance with virtue against vice" , "In mediaeval show" .)