Pressure forced sister to carry on (7)
I believe the answer is:
persist
'carry on' is the definition.
(to persist is to carry on with something)
'pressure forced sister' is the wordplay.
'pressure' becomes 'p' (scientific abbreviation).
'forced' is an anagram indicator.
'sister' with letters rearranged gives 'ersist'.
'p'+'ersist'='PERSIST'
'to' is the link.
(Other definitions for persist that I've seen before include "Continue firmly or obstinately" , "Keep trying" , "Show doggedness" , "Prevail" , "Refuse to stop" .)