Second hospital admits being on strike to make a point (5)
I believe the answer is:
south
'a point' is the definition.
(I know that south is a type of cardinal compass point)
'second hospital admits being on strike' is the wordplay.
'second' becomes 's' (common abbreviation).
'hospital' becomes 'H' (abbreviation for hospital on maps).
'admits' is an insertion indicator (to admit is to allow in).
'being on strike' becomes 'out' (I've seen this before).
's'+'h'='sh'
'sh' placed around 'out' is 'SOUTH'.
'to make' acts as a link.
(Other definitions for south that I've seen before include "1949 musical by Rodgers and Hammerstein, made into a film in 1958" , "Direction to the right of sunrise" , "Compass point" , "Antarctica" , "Down on a map" .)