Direct answer
An agency should consider retained search when a role is senior, confidential, commercially important or difficult enough that relying on advert response and whoever happens to be actively looking is unlikely to solve it properly.
When does retained search earn its keep?
If you're hiring an important leader, entering a new market, replacing somebody confidentially or looking for a very specific combination of experience, the people you want may never apply to your advert.
That's when properly mapping the market becomes much more valuable.
What changes with retained search?
The recruiter has a proper mandate to search the market rather than racing other agencies to send the first CV.
That creates more room for:
A deeper brief
Proper market mapping
Direct approaches to passive candidates
More detailed assessment
Consistent candidate management
Honest market feedback
And a process where everybody has a bit more skin in the game.
When is it probably overkill?
If the role is straightforward, the candidate market is healthy and a normal specialist recruitment process is likely to solve it, retained search may be unnecessary.
David will tell you that too.