Clerical magic, in contrast to that of magic-users, is noted for being "divinely given," thereby freeing the cleric from having to study to learn them. This would seem to be a reference to the Chance to Know table based on Intelligence rather than an account of how spells are memorized by clerics. There's in fact no explanation given for how long one must rest, if at all, after exhausting one's daily complement of clerical spells, so one must assume that it's similar to that of magic-users.
Holmes details eight first and eight second level spells, although, as he notes "Second level spells are not available to clerics of below fourth level, and are included for use with non-player characters and scrolls." This is in contrast to the 3rd-level MU spells, which he lists only by name but provides no descriptions for.
Of the 1st-level spells, two are new: remove fear and resist cold. Cure light wounds follows OD&D but with the added detail that "the cleric must touch the wounded person to heal him." Detect evil and detect magic are identical to their MU counterparts, as are light, protection from evil, and purify food and water. Remove fear is an interesting spell, because, despite its name, it does not remove fear but instead grants a bonus to a saving throw against fear equal to the level of the cleric. Someone who is already failed a save and become afraid when remove fear is cast upon him gains a second saving throw at the appropriate bonus. Resist cold, meanwhile, gives both a flat bonus to saves versus cold and a reduction of -1 per die of cold damage dealt.
Of the 2nd-level spells, two are new here as well: know alignment and resist fire. Bless follows OD&D, right down to the bonus to morale, a concept Holmes treats only obliquely in his rulebook. Find traps and hold person likewise follow the LBBs. Know alignment is, as noted, new and it's, in my opinion, a terrible spell that runs counter to the treatment of alignment in both OD&D and in Holmes. The spell doesn't merely let the caster know the target's alignment (i.e. Lawful Good, Chaotic Evil, etc.), but also "how lawful or chaotic, good or evil, a creature is." It's silly and problematic on many levels and I think D&D was better as a game without it.
Resist fire functions nearly identically to resist cold, except that it states it allows the target to "resist normal fire for a maximum of 2 melee rounds," while resist cold allows one to resist freezing temperatures "while the effects of the spell last," which is 6 turns. Granted, there's a common sense difference between mere freezing temperatures and fire but, still, I find it noteworthy that resist fire is a better spell. Of course, it's also 2nd-level, so perhaps that explains it.
Silence, 15' Radius functions as in Supplement, but includes a note that conversation is impossible while under its effects. No mention is made of its effect on spellcasting, although there's good reason to assume, based on other passages, that it would negate it as well. Both snake charm and speak with animals follow OD&D.
Holmes continues the tradition of giving evil clerics (no longer called "anti-clerics") reversed versions of several spells. The implication of the text -- "Evil clerics have basically the same spells as do good clerics. However, spells in italics are reversed for evil clerics." -- is that evil clerics cannot cast, for example, cure light wounds at all, being limited to cause light wounds instead. The list of reversed spells is the same in Holmes as in the LBBs, although the spells are explicitly given names here (Curse as the reverse of bless, for example). What's interesting is that, while there's no reversed version of protection from evil included, there is a detect good. I find this intriguing as detect evil detects only "evil thought or intent," a description that could be viewed in a relative fashion, with "evil" meaning only "antagonistic." That doesn't seem to be the case here, although, honestly, it's hard to tell just what detect good would detect and what use that knowledge would be to an evil cleric. In any case, it's further evidence that, by the time of Holmes at least, alignment had undergone enough permutations of meaning that it was on its way to becoming incoherent, both mechanically and as a game world construction.