My family member provides a connection (11)
I believe the answer is:
correlation
'a connection' is the definition.
(thesaurus)
'my family member' is the wordplay.
'my' becomes 'cor' (both are expressions of surprise).
'family member' becomes 'relation' (a relation or relative).
'cor'+'relation'='CORRELATION'
'provides' acts as a link.
(Other definitions for correlation that I've seen before include "Interdependence or the degree of it" , "Link" , "Interdependence (of statistical variables)" , "Mutual relationship of interdependence" .)