Looked into dust storm, initially in equatorial desert (7)
I believe the answer is:
studied
'looked into' is the definition.
(to look into something is to study it)
'dust storm initially in equatorial desert' is the wordplay.
'storm' indicates anagramming the letters.
'initially' says to take the initial letters.
The initial letters of 'in equatorial desert' is 'ied'.
'dust' anagrammed gives 'stud'.
'stud'+'ied'='STUDIED'
(Other definitions for studied that I've seen before include "Tried to learn" , "deliberate" , "Scrutinised" , "Well-considered" , "Learnt by reading" .)