Sign diaries with no name! (5)
I believe the answer is:
aries
'sign' is the definition.
(star sign)
'diaries with no name' is the wordplay.
'with no' is a deletion indicator.
'name' becomes 'Di'.
'diaries' with 'di' removed is 'ARIES'.
(Other definitions for aries that I've seen before include "House" , "Zodiac ram" , "Sheep" , "A sign from Heaven" , "Zodiacal sign also known as the Ram" .)