Acabei de encontrar a resposta aqui:Como alternar com um array no MySQL?
set @billable_types = 'client1,client2,client3';
select * from mttl where find_in_set(mttl.type, @billable_types);
set @billable_types = 'client1,client2,client3';
select * from mttl where find_in_set(mttl.type, @billable_types);