Looking unhappy about navy at the third level (7)
I believe the answer is:
ternary
'at the third level' is the definition.
(relating to the number three)
'looking unhappy about navy' is the wordplay.
'looking unhappy' becomes 'teary'.
'about' means one lot of letters goes inside another.
'navy' becomes 'rn' (abbreviation for Royal Navy).
'teary' going around 'rn' is 'TERNARY'.
(Other definitions for ternary that I've seen before include "Relating to a third order" , "Composed of three parts" .)