Long after lay he musing at her mood,/ Much grieved to thinke that Gentle Dame [Una] so light. (I.i.55)
Victim to Archimago's trickery, Redcrosse believes Una has betrayed him, the first moment of (apparant) disloyalty in the poem—and it cuts deep.
For wondrous anguish in [Arthur's] hart it wrought,/ To see his loved Squyre into thralldom brought. (I.viii.15)
Arthur and his squire, Timias, are bros. This is one of many moments in the poem where their loyalty ensures that they help each other out.
So courteous conge both [Redcrosse and Guyon] did give and take,/ With right hands plighted, pledges of good faith. (II.i.34)
In a classic moment of vowing eternal friendship, Redcrosse and Guyon must part and go their separate ways… but they maintain the link of loyalty.
But his good Squire him helping vp with speed,/ With stedfast hand vpon his horse did stay,/ And led [Arthur] to the Castle by the beaten way. (II.xi.48)
Another instance of Arthur-Timias love, but this time around its Timias who saves Arthur—it works both ways in this whole "loyalty" system.
Thus reconcilement was betweene [Britomart and Guyon] knit,/ Through goodly temperance, and affection chaste,/ And either vowd with all their power and wit,/ To let not others honour be defaste. (II.i.12)
Britomart and Guyon did not start things out on the right foot—she knocked him off his horse—but in the land of chivalry, that doesn't mean two good knights can't patch things up and vow eternal friendship.
The warlike virgine seeing his so prowd/ And boastfull chalenge, wexed inlie wroth… And sayd, her loue [Amoret] to lose she was full loth,/ But either he should neither of them haue, or both. (IV.i.10)
Britomart shows her loyalty to Amoret by assuming the attitude of a knight defending his right to protect his beloved—there doesn't really seem to be the same language available to Britomart to describe the loyalty between two female friends.
But euermore, when [Agape] fit time could fynd,/ She warned [her sons] to tend their safeties well,/ And loue each other deare, what euer them befell (IV.ii.53)
The trio of brothers—Priamond, Dyamond, and Triamond—certainly take their mother's command to be loyal to heart. The first two brothers ultimately lose their lives in order to help out brother #3.
All ouercome with infinite affect,/ For [Calidore's] exceeding courtesie, that pearst/ [Briana's] stubborne hart with inward deepe effect,/ Before his feet her selfe she did proiect,/ And him adoring as her liues deare Lord,/ With all due thankes, and dutifull respect,/ Her selfe acknowledg'd bound for that accord/ By which he had to her both life and loue restord. (V.i.45)
Briana, great stealer of people's hair, turns out to be an unlikely example of loyalty to Arthegall, after realizing he did her a solid by ordering Crudor to marry her.
But I am bound by vow, which I profest/ To my dread Soueraine, when I it assayd,/ That in atchieuement of her high behest,/ I should no creature ioyne vnto mine ayde/ For thy I may not graunt, that ye so greatly prayde. (VI.ii.37)
Although Calidore would really like Tristram to join him in his quest for the Blatant Beast, his vow to the Faerie Queene stipulated that it was a one-man-task (we're not sure why) and Calidore is super loyal to his Queen… at least in the beginning.
Tho gan Sir Calidore him to aduize/ Of his first quest, which he had long forlore;/ Asham'd to thinke, how he that enterprize,/ The which the Faery Queene had long afore/ Bequeath'd to him, forslacked had so sore. (VI.xii.12)
After saving Pastorella and gaining her hand in marriage, Calidore suddenly remembers this whole quest-thing he vowed to the Faerie Queene, and his loyalty to her starts to make him feel mighty guilty about his extra-long detour.