FI's with out CPL TK do they get FCL 945 privileges
 

Just pulled the following of the excellent ontrack website

"Which instructors can gain FCL.945 privileges ?
FI* and CRI who have the privilege to instruct for SE and/or TMG class ratings. Some EASA States limit the number of instructors with FCL.945 privileges and some States carry out a selection process

*FI restricted to teaching for the LAPL only may not qualify for the privilege"

So does that mean that FI'ls without CPL TK don't get FCL 945 privileges? and if thats the case what do they have to do to qualify?

As a CRI who can be issued with a FCL945 endorsement does not require CPL TK, then that would not appear to be a relevant criteria for not giving it to a FI without CPL TK!
As I understand it, any CRI or FI who has CAA admin action necessitating the reissueof a licence, then FCL.945 will be added automatically. In any other case you request it and pay the appropriate fee (currently £56).

Apply for a CRI certificate.

The bigger picture is that Part-FCL only considers Part-FCL licences. As the 'LAPL-only' FI may not provide any instruction for holders of SEP Class Ratings, there is no need for 'LAPL-only' FIs to have FCL.945 privileges because no entries are made in a LAPL - there's nothing to sign!

Of course in the UK, instructors with FCL.945 privileges may also sign revalidation entries in NPPLs, but that's of no concern to Part-FCL per se.

Assuming a 'LAPL-only' FI also meets the prerequisites for a CRI certificate, then such an FI should certainly apply as Whopity suggests.

There are of course FIs without CPL TK who are not confined to LAPL only instruction i.e. those with grandfather rights, Ex BCPL holders.