Buttoned-up (4)
(Other definitions for prim that I've seen before include "Affectedly dainty or refined" , "Demure" , "Old-maidish" , "Proper or prissy" , "Straight-laced" .)
(Other definitions for aloof that I've seen before include "Distant or stuck-up" , "Unapproachable, distant" , "rather cold" , "Disinterested" , "Detached, distant" .)