To stick to something is a phrasal verb which means you do what you say you are going to do.
For example, my neighbours have recently complained about me singing in the shower and although I don’t completely understand why they don’t appreciate my musical renditions of American rap music, I did make a promise to them to try to stop. However, sticking to this promise is driving me around the bend so now I have to stick a flannel in my mouth to prevent me from belting out a tune.
In hindsight, I should have told them to shut up complaining and put ear plugs in. Seriously, life without music just isn’t right unless of course Celine Dion is singing and then I’d rather slit my own wrists. All that romantic ‘jibber jabber’ and ‘I can’t go on without you’ just gets on my nerves! Am I right, or what?!