Visitor I finally defeat is to reckon without specific thought (10)
I believe the answer is:
guestimate
'specific thought' is the definition.
'guestimate' can be an answer for 'thought' (guestimate is a kind of thought). I'm unsure of the 'specific' bit.
'visitor i finally defeat is to reckon without' is the wordplay.
'visitor' becomes 'guest' (someone visiting a place).
'finally' says to take the final letters.
'is to reckon' becomes 'mae' (I am not sure about this - if you are sure you should believe this answer much more).
'without' indicates putting letters inside.
The final letter of 'defeat' is 't'.
't' going within 'mae' is 'mate'.
'guest'+'i'+'mate'='GUESTIMATE'
Can you help me to learn more?
(Other definitions for guestimate that I've seen before include "Result of rough calculation" , "Rough judgment" , "punt" , "Rough value" , "rough idea" .)