Just because one partner has a high need for sex, doesn't mean the other partner should expect them to always meet that need. Perhaps your character should do some soul searching to figure out why their partner is not interested in them? Is your partner going through something that makes intimacy not as important? Make sure first there isn't a problem with the relationship. If the relationship is solid but your partner just doesn't need or want sex as much as you then figure out how to work that out on your own, either through masturbation, exercise, whatever. But you start with being honest with your partner about your need for more frequent sex and then go from there. It also depends on how frequently you NEED sex. If you NEED it multiple times daily, every single day, you may actually have a sexual addiction problem which needs to be addressed.
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I wonder why people keep saying to leave the marriage/Relationship. Sex is important but is it the only reason you got married? How about love? Understanding? Try to know what's up with the person. Maybe he or she is going through some hard time. Or go for couple therapy. Do all you can, and be patient. If you can't hold yourself, do what you can to relieve yourself or better still try to not think about sex. It's hard I know but common we have all had times in our lives when we were younger and when we lived many months without sex. Sex is good but isn't enough reason to leave a marriage just like that, without trying first, especially if your partner didn't cheat on you.
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(I'm treating this as a serious question about literature). There are myriad ways, depending on how confronting you want the work to be. Masturbation is a novel idea but might be tricky to work a good story around it. Cheating/polyamoury is the obvious one so you'd need to write in a twist somehow that hasn't been used in the last few millennia; maybe it turns out with a happy ending (pun intended). If you want your work to be truly disturbing, incest, bestiality and the like could work (eg a twist on Oedipus). I'd also suggest an unreliable narrator if it's in first-person, but make it really subtle. If you want to make readers feel really uncomfortable, I'd suggest reading The War Zone (also a brilliant film).
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Is the "high urge" too much to cope with, like wanting it 5 times a day? If someone wanted sex from me that frequently I'd be telling them to do it themselves and go see a therapist because it's a bit OTT. If it's a more usual level then I'd initiate a discussion about it within the relationship to see if something could be sorted out to please the both of us. If I was simply not interested in sex at all, with anyone, and felt it was a chore to perform or a duty, I'd talk about different ways of being intimate and loving. If I was truly asexual, I would not have a problem with my partner having to involve a third party as long as they didn't bring them home and do it in our bed, unless I was also attracted to them (but if that was the case we probably wouldn't have an issue). But that's just me, I'm pretty open minded about sex. I would not ask my partner to live without sex because I wasn't interested, and I would not want my partner to treat me as a tool for their satisfaction whenever they wanted.
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Well I have a theory if he/she is not doing you and is reasonably attractive he/she is probably doing someone else (unless an emotional or medical issue including hormone or mental illness is causing this)...I would have the character get paranoid about them having an affair...me personally if my partner is not having sex with me, and no medical/emotional reason he shared with me, I would leave. But I’m not married and I don’t have financial issues to prevent me. So the question is kind of too vague depending what your characters socio/eco situation is and what their personality is, their age, kids, marital status etc.