Promise to keep a hold of extremely tense jumper (7)
I believe the answer is:
sweater
'jumper' is the definition.
(both can mean an item of clothing)
'promise to keep a hold of extremely tense' is the wordplay.
'promise' becomes 'swear' (I've seen this before).
'to keep a hold of' is an insertion indicator (inserted letters are held).
'extremely' means to remove the middle letters (only the extremes of the word are used).
'tense' with its middle removed is 'te'.
'swear' enclosing 'te' is 'SWEATER'.
(Other definitions for sweater that I've seen before include "Re waste: it's a garment" , "A present from Mum!" , "Jumper (7)" , "Top" , "Knitted upper garment" .)