We have a number of runs from someone who was banned from a different game, Do we accept the runs? We have no idea why he was banned but we know what game he was banned from.

Don’t ban them unless they are actually cheating in the game you moderate.

According to the Moderation Rules:

"It is left to the game moderators to decide whether they want to track runs played by users banned from the site or not."

Depends on why they are banned on the other game. There can be various reasons and some things wouldn't even lead to bans in other communities. Just straight out banning someone from your game without knowing the reason? No, I wouldn't do that. If he was for example caught splicing together runs - yes, I would ban him as well and hoenstly expect a sidewide ban (which doesn't automatically happen).

So the person in question is Banned indefinitely, they did something on another game which got them banned, they have registered for a alt account and posted speedruns on that account, we have had complains from other people about this person because they used to cheat in the Dead by Daylight, (we have no proof on this so nothing was done).

He has never (AFAIK) cheated his runs on DBD.

[quote=Site Rules]You are permitted to have exactly one account on the site. Alternate accounts will be banned.[/quote]

If the person in question got banned from speedrun.com as a whole and then created a new account to continue interacting with the site, then that amounts to Ban Evasion and is not allowed.

Under that specific circumstance, I'd just report the account to the Support Hub explaining and giving evidence about this connection between the new account and the previous one and let the site mods deal with it.