Invest capital, perhaps (7)
I believe the answer is:
'invest' is the definition.
(I've seen this before)
'capital perhaps?' is the wordplay.
I cannot really see how this works, but
'perhaps?' could be 'eg' (for example) and 'eg' is found within the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for besiege that I've seen before include "Surround (town etc) with armed forces" , "Crowd round oppressively" , "Surround (a place) with hostile intent" , "Surround (a place) in war" , "Surround - harass" .)