Sort of look designed to cheer him? (4-6)
I believe the answer is:
Here is my best explanation:
'sort of look' is the definition.
(a come-hither look displays romantic interest)
'designed to cheer him?' is the wordplay.
'designed' indicates an anagram (designed with the letters).
'tocheerhim' anagrammed gives 'COME-HITHER'.
(Other definitions for come-hither that I've seen before include "Seductive", "Coquettish" and "Alluring".)