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 subsidiary indication.
'designed' is an anagram indicator (designed with the letters).
'tocheerhim' with letters rearranged gives 'comehither'.
(Other definitions for come-hither that I've seen before include "Coquettish" and "Alluring".)