Sappers permitted to enter gym that's full (7)
I believe the answer is:
replete
'full' is the definition.
(synonyms)
'sappers permitted to enter gym' is the wordplay.
'sappers' becomes 're' (Royal Engineers).
'permitted' becomes 'let' (I've seen this before).
'to enter' means one lot of letters goes inside another.
'gym' becomes 'pe' (short for Physical Education).
'let' inserted inside 'pe' is 'plete'.
're'+'plete'='REPLETE'
'that's' acts as a link.
(Other definitions for replete that I've seen before include "Sated by food" , "Stuffed, gorged, sated" , "Full, sated" , "Well-fed" , "charged" .)