
Tbh I wouldn't take him to a vet, (a) they charge a fortune and (b) they often don't seem to know what they're doing. I've lost count of the number of snappy dogs I trim nails where I have to muzzle because the owner took them to a vet or vet nurse and they cut all the quicks and traumatised the dogs. A Clumber has probably got white nails, so you can easily do it yourself. Get a groomer to show you or do it with you watching the first time, I wouldn't charge more than £5 to just do nails, it only takes a few minutes even with a wriggly puppy. Then you can pick a time when he's quite tired and cuddly, and get him on your lap, just gently hold a paw and snip off the tip, making sure you stay away from the pinkish bit which will be the quick and will hurt and bleed if you catch it. If there's more than one of you, one person can give a 'restraining cuddle' and help hang on to spare paws while the other one trims. And of course doing it at home, you can do one foot, then give a treat and let him go and do the next foot next day and so on. Don't forget the dewclaws if he has them, normally just on front feet.
With the fur under the pads it's a similar thing - you might also want to get him used to standing or lying on a table, depending on how much generall trimming you want to do, but otherwise just check under and between his pads. Spaniels are prone to getting mud or grass seeds caught in the fluff under the feet and I often get dogs in with mud and hair packed into a hard lump, must be like walking with stones in your shoes for the dog!