Letter tiles arranged by each person, initially (7)
I believe the answer is:
epistle
'letter' is the definition.
(epistle is a kind of letter)
'tiles arranged by each person initially' is the wordplay.
'arranged' is an anagram indicator (letters rearranged).
'by' is a charade indicator (letters next to each other).
'initially' says to take the initial letters.
The first letters of 'each person' is 'ep'.
'tiles' with letters rearranged gives 'istle'.
'istle' put after 'ep' is 'EPISTLE'.
(Other definitions for epistle that I've seen before include "Such as St Paul wrote" , "a for instance" , "Missive; letter" , "A letter from St Paul" , "Paul's work" .)