Selecting lists where all are prime

This is a perfect use case for AllTrue:

Select[t, AllTrue[PrimeQ]]
(* {{7, 13, 19}, {37, 73, 109}} *)

Alternatively, you should specify the pattern you actually want in Cases:

Cases[t, {___?PrimeQ}]
(* {{7, 13, 19}, {37, 73, 109}} *)

If for some reason you really want a function you can Map over the list to do what you want, you'll need to use Replace in concert with the special symbol Nothing:

Map[Replace[Except[{___?PrimeQ}] -> Nothing], t]
(* {{7, 13, 19}, {37, 73, 109}} *)

Pick[t, And @@@ PrimeQ @ t]

{{7, 13, 19}, {37, 73, 109}}

Either of these takes advantage of the fact that PrimeQ automatically threads over lists:

Select[t, Apply[And]@*PrimeQ]
Select[t, And @@ PrimeQ[#] &]

(* Out: {7, 13, 19}, {37, 73, 109} *)