Too stifling a covering (7)
I believe the answer is:
overlay
'covering' is the definition.
(overlay is a kind of covering)
'too stifling a' is the wordplay.
'too' becomes 'overly' (synonyms).
'stifling' means one lot of letters goes inside another.
'overly' going around 'a' is 'OVERLAY'.
(Other definitions for overlay that I've seen before include "Lie on top of; covering" , "Put on top of something else" , "Cover" , "Blanket" , "put on coat" .)