I think the official way to do this is to do:
$client = Client::find(1);
$exists = $client->products->contains($product_id);
It’s somewhat wasteful in that it’ll do the SELECT query, get all results into a Collection and then finally do a foreach over the Collection to find a model with the ID you pass in. However, it doesn’t require modelling the pivot table.
If you don’t like the wastefulness of that, you could do it yourself in SQL/Query Builder, which also wouldn’t require modelling the table (nor would it require getting the Client model if you don’t already have it for other purposes:
$exists = DB::table('client_product')
->whereClientId($client_id)
->whereProductId($product_id)
->count() > 0;