Look into first of rooms: see drunken principal (8)
I believe the answer is:
research
'look into' is the definition.
(researching is a kind of looking into)
'first of rooms see drunken principal' is the wordplay.
'first of rooms' becomes 'r' (1st letter of 'rooms').
'drunken' indicates anagramming the letters.
'principal' becomes 'arch' (as in arch-enemy).
'see' anagrammed gives 'ese'.
'r'+'ese'+'arch'='RESEARCH'
(Other definitions for research that I've seen before include "scientific survey" , "university job" , "Experimentation" , "Investigation designed to expand knowledge" , "Scientific investigation" .)