Very poor leader of Senate cornered (8)
I believe the answer is:
strapped
'very poor' is the definition.
(strapped for cash)
'leader of senate cornered' is the wordplay.
'leader of' suggests taking the first letters.
'cornered' becomes 'trapped' (synonyms).
The first letter of 'senate' is 's'.
's'+'trapped'='STRAPPED'
(Other definitions for strapped that I've seen before include "Needy - secured" , "broke" , "not generating enough cash?" , "beaten" , "affected by shortage" .)