This is mainly a question regarding a largely cinematic sort of deal, but are there any rules regarding Psychic clashes in Dark Heresy? I'm largely referring to great "Beam of War" clashes or the like. Or is this largely up to the GM in question. An example of what I'm referring to, might, say, in the event of two Psykers fighting, one Psyker using a Delayed Action to launch a burst of Bio Lightning into the opposing Psyker's Fire Bolt.

Or is this not possible to do/not intended in any of the rulebooks? I just think it'd be a very cool thing to do for cinematic purposes, perhaps being "resolved" by opposing Willpower tests or the like? If there's no rules regarding this sort of thing I might discuss it with my GM for the purpose of house rules, but wanted to figure out if there was any rule on this sort of thing that I may have missed.

You're looking at a homebrew there. A number of Opposed Willpower Tests would probably do

I would base it off the Lidless Stare rules for Navigators in Rogue Trader. They even have a formalized version of it in the Navis Primer. I'd suggest checking those two out for some inspiration on how to handle a psyker duel of minds. (Page 180 Rogue Trader Core Rulebook, the Lidless Stare) and (page 41, Navis Primer, Navigator Duels)

This is mainly a question regarding a largely cinematic sort of deal, but are there any rules regarding Psychic clashes in Dark Heresy? I'm largely referring to great "Beam of War" clashes or the like. Or is this largely up to the GM in question. An example of what I'm referring to, might, say, in the event of two Psykers fighting, one Psyker using a Delayed Action to launch a burst of Bio Lightning into the opposing Psyker's Fire Bolt.

Or is this not possible to do/not intended in any of the rulebooks? I just think it'd be a very cool thing to do for cinematic purposes, perhaps being "resolved" by opposing Willpower tests or the like? If there's no rules regarding this sort of thing I might discuss it with my GM for the purpose of house rules, but wanted to figure out if there was any rule on this sort of thing that I may have missed.

Watch the movie scanners. That will be all you need.

This type of thing falls under GM discretion and "rule of cool." Most GMs will allow something like this to happen simply because it promotes fun and creative play. While it may not be in the rules, the GM is there to facilitate the situations of "why not?'

I would put it at a series of opposed willpower tests where you tally up degrees of success until one psyker is clearly overpowering the other, causing the other psyker to fly back as his powers or overwhelmed by the power of your PC.