Palindromes pop up in cryptic crosswords every now and usually use a simple format of having an indicator that suggests the fodder will not change whichever way it is read. It is worth noting that palindromes sometimes do not have a subsidiary indication other than their indicator.
To indicate the palindrome NOT ON the setter may write:
not on whichever way you look at it ...
... here the indicator is WHICHEVER WAY YOU LOOK AT IT which indicates the words is the same back to front as it is front to back
Any word or phrase that fairly indicates the fodder is the same when read either way may be used to indicate a palindrome. Here are some more examples:
Palindrome indicators: BACK AND FORTH/UP AND DOWN
Note that the former would be suitable for and across clue, the latter a down.
Here is an example:
Stories that can be read either way (5)
stories - definition
that can be read either way - palindrome indicator (a palindrome reads the same back to front as it does front to back.)