Old scientist gives girl a sign about his heart (7)
I believe the answer is:
galileo
'old scientist' is the definition.
(Galileo Galilei, 1564-1642)
'girl a sign about his heart' is the wordplay.
'girl' becomes 'gal' ().
'a sign' becomes 'Leo' (star sign).
'about' says to put letters next to each other.
'heart' indicates the central letters.
The middle of 'his' is 'i'.
'leo' put after 'i' is 'ileo'.
'gal'+'ileo'='GALILEO'
'gives' acts as a link.
(Other definitions for galileo that I've seen before include "Italian astronomer, a founding father of modern science" , "Famous Italian" , "US unmanned space-craft launched in 1989 to investigate Jupiter" , "Great Italian astronomer and physicist of 17th century, suppressed by Church" , "Astronomer - ogle Ali (anag)" .)