There is a reason why intelligence is not usually something that arises from selection pressures purely via predator-prey relationship. For a predator, it is usually more "cost-effective" to get immediate results by evolving larger claws, specialized teeth, bigger muscles, better digestion, camouflage, better vision, whatever physical enhancement they can get without sacrificing basic health and reproductivity. Similarly for prey, it's easier to evolve traits that will ensure they can pass their genes on better - faster run, body armour, horns, spikes, more camouflage, poison, herding behaviour. We have been having this kind of arms race since life evolved on earth and needed energy from somewhere for sustenance.
Intelligence is expensive. You need extra energy to sustain an organ/synaptic system/processing network (aka brain); you need that extra energy evenly all around the year, not just seasonally; you need to be able to sustain this added body weight of the above without compromising your survival ability; you may take much longer to develop and mature. Think about us - human females have dangerous and painful labour just to be able to deliver large-headed babies who need long gestation periods to develop; babies need a long period of education and protection before they are able to survive by themselves; we as people are interdependent on each other and our social constructs for even our basic daily needs; none of us can (without help, protection and tools) fight and survive against lions, tigers, wolves or even a pack of feral dogs. Our intelligence has come with a great 'expense' and the push towards intelligence needs to justify that expense. There has to be something so valuable that is gained that getting intelligence is worth more than getting physical adjustments.
Possible extra selection pressure for intelligence could come from:
1. Climate change and environmental stress. Look at human evolution - we are champion generalists, able to adapt to any environment. Being adaptable means being able to make changes on the fly, asap, comapared to the thousands and millions of years it takes to evolve traits and changes by which time the situation may be wildly different. Evidence points we evolved this ability during a time of severe environmental change. Are your predators-prey living on a highly changing environment where they need to make quick decisions with limited basis in past behaviour/experience?
2. Manual dexterity and ability to explore and make tools. 335
Consider the octopus. Very limited interaction, if any, with parents, neural network distributed all over the body including limbs, mostly solitary, predator as well as prey, short-lived, nothing like the typical example of intelligent mammal we usually use to demonstrate intelligence. Still very intelligent and known to use tools. Any creature would need specialized appendages to explore and manipulate its surroundings. Having a sensory network to process, manipulate and make sense of the world around seems to be enough of a jumpstart to making ideas to change the "world" to suit better. Are your creatures living in a tactile world that can stimulate their curiosity and have appendages that can manipulate it to suit themselves?
3. Continued access to nutritious food. Getting energy sources that can sustain a power-hungry brain and then getting the brain to think up new ways to getting that nutritious food, especially if it's not easily obtained (eg. bone marrow from scavenged prey, tools, fire). Omnivores and generalists have a advantage here. Sure, predators get a lot of nutrition but if their prey base is limited, they will only specialize towards better ways of catching that.
4. Complex social structure and some form of 'language' or shared code of information storage. To survive tough times. Our vocal chords and linguistic ability may have started us on an upward spiral where getting smarter was the direct result of... getting smarter.
I can understand that these examples are a bit earth-bound but the basic question is still the same: sure, intelligence is cool but expensive to maintain; there needs to be something special to get it started. 335