Colin, giving away nothing, in charge of private hospital (6)
I believe the answer is:
clinic
'private hospital' is the definition.
(clinic can mean a health care centre)
'colin giving away nothing in charge' is the wordplay.
'giving away' is a deletion indicator.
'nothing' becomes 'O' (looks like zero - 0).
'in charge' becomes 'ic' (abbreviation for 'in charge').
'colin' with 'o' taken away is 'clin'.
'clin'+'ic'='CLINIC'
'of' acts as a link.
(Other definitions for clinic that I've seen before include "Medical resource" , "Healthcare facility" , "Place for specialised treatment, from doctor or politician" , "Private hospital" , "Place for medical treatment or political advice" .)