"To a Mouse" has two inferred promises. Burns, saddened that he has disturbed this little mouse's winter home with his ploughing, promises that he will not begrudge the little creature what corn of his she can manage to save: he says he will not miss it.
I doubt na, whiles, but thou may thieve;
What then? poor beastie, thou maun live!
A daimen icker in a thrave
‘S a sma’ request;
I’ll get a blessin wi’ the lave,
An’ never miss’t!
He also says that he sympathizes with the mouse, feeling in much the same circumstances as she: trying to survive. In this case, he feels regret for the panic he has caused her and says he will not like others, chase her and try to kill her.
WEE, sleekit, cow’rin, tim’rous beastie,
O, what a panic’s in thy breastie!
Thou need na start awa sae hasty,
Wi’ bickering brattle!
I wad be laith to rin an’ chase thee,
Wi’ murd’ring pattle!
I am assuming that you are perhaps referring to the 5th verse of the 1st stanza, which says:
I wad be laith to in an' chase thee
Wi' murd'ring pattle!
In plain English that basically means that what worth could he get from chasing the mouse and killing it, therefore, he is promising the mouse that he will not kill or chase it out.
Another promise is that he will allow the mouse to be in peace, as he understands the needs of any living thing to survive the best way they can. After all, this is a poem created for the underdog, the oppressed, and those who literally live off the drags of others.