I bought a house that has a sink outside by the grille. The sink drains very slowly. There is no vent on the drain line. Would this cause the extremely slow draining?

If so, can I add a vent inside the cabinet, under the counter top?

i bought a house that has a sink outside by the grille. the sink drains very slowly. there is no vent on the drain line. would this cause the extremely slow draining?

if so, can i add a vent inside the cabinet, under the counter top?

Yes, You can cut in a tee after the trap and just run a "local vent" up the wall -OR- you may add a AAV,(Air Admittance Valve) cheater vent,(see image) just after the trap. Both Studor and Oatey sell AAVs You may put those names into a search engine to find out more about them. Good luck, Tom