One of the appeals in the idea of a romance between two people separated in age by many years is that one can be a guide for the other, being able to speak from experience. This is almost always present on a subliminal level in Doctor Who but becomes explicit in "The Girl in the Fireplace", a Tenth Doctor episode from 2006. Widely regarded as one of the best episodes of the relaunched series, it's not hard to see why--in addition to the romance element it packs in several other effective things, including clockwork "droids", some great locations not managing (but admirable in the effort) to stand in for Versailles, and some delightfully gruesome and scary body horror.
I love the concept of robots using human body parts to repair a ship, their priorities so mixed up that they don't see the logical inconsistency in serving humans in this way. Scavenging human body parts to repair technology was of course what the Tractators wanted to do in Frontios but the new relaunched series had liberty to show it much more explicitly.
And they want the brain of Madame de Pompadour (Sylvia Miles) to finish the job. When the Doctor (David Tennant) sees her as a little girl (Jessica Atkins) through an 18th century French fireplace somehow aboard a spaceship in the distant future, he's visibly confused but also comforting and wise. Tennant as a performer, as always, strikes just the right balance of impossibly wise and disarmingly silly. I love how he pauses when trying to think of a job for himself that would explain his presence in the fireplace to the little girl.
Very quickly (for the Doctor), the handsome dream man becomes a mysterious and charismatic gentleman for the adult Madame de Pompadour. Writer Steven Moffat would later reuse this basic concept for the first Eleventh Doctor episode--the main difference being that Amy Pond does become a companion and Madame de Pompadour is prevented from doing so. Also, the Eleventh Doctor refuses Amy's romantic advances on the grounds of their age difference.
That is the other side of the coin--an older partner may provide a sense of security, acting partly as parent, but that also means there's an inevitable barrier between the two people, particularly when it comes to the Doctor, who's over a thousand years old. The younger partner can benefit from her elder's experience but, for that very reason, she can't understand what it's like to have had so much experience. "The Girl in the Fireplace" attempts to overcome this with a sort of mindmeld sequence in which Madame de Pompadour witnesses the Doctor's childhood. After this, there's a jump cut to the Doctor rescuing his friends, apparently inebriated, and boasting about how great it is to party with the French.
I'm not sure the mindmeld thing was really necessary as the story works better seeing their relationship as one of casual sex between two people who have somewhat unusual reasons for their clear chemistry. Though Steven Moffat has denied in interviews that the two actually had sex in that jump cut, he certainly can't stop us imagining it, and I'm pretty sure we all did. And, as in horror, the mere hint of a thing typically has more of an impact than showing it.