Soldiers permitted to enter gym that's full (7)
I believe the answer is:
replete
'full' is the definition.
('replete' can be a synonym of 'full')
'soldiers permitted to enter gym' is the wordplay.
'soldiers' becomes 're' (Royal Engineers).
'permitted' becomes 'let' (I've seen this before).
'to enter' is an insertion indicator.
'gym' becomes 'pe'.
'let' inserted within 'pe' is 'plete'.
're'+'plete'='REPLETE'
'that's' acts as a link.
(Other definitions for replete that I've seen before include "Chock-a-block" , "unable to take any more" , "Filled to satiety" , "Filled, well supplied" , "Stuffed, gorged, sated" .)