That from the nunnery Of thy chaste breast, and quiet mind, To war and arms I fly. (2-4)
The speaker speaks of his sacrifice of love for battle in the form of these lines; "nunnery" and "fly" rhyme (or at least they did, once upon a time), and the speaker is sacrificing the former (along with its "quiet," peaceful setting) for the latter (the heat of battle, the haste associated with the word "fly").
True, a new mistress now I chase, The first foe in the field; And with a stronger faith embrace A sword, a horse, a shield. (5-8)
Notice that they key words "chase" and "embrace" can refer to acts of love (chasing a woman, embracing a woman) and acts of war (chasing an enemy, embracing weapons). The speaker is giving up a certain type of chasing and embracing for another very different one. But for him, the emotions surrounding the whole thing are the same.
I could not love thee, Dear, so much, Loved I not honour more. (11-12)
The speaker's sacrifice is necessary if he is to be taken seriously as a man; if he didn't love "honour more," then he wouldn't be able to love Lucasta, which implies that sacrifice is a necessary part of love, or rather being willing to sacrifice things for your principles is an important part of being able to love.