Can we grow a community online if we trademark that

A trademark won't help you build a community per se. A trademark just means no one can use your trademark in your industry. If you've got a great name trademark it and then try to brand it.

But building a community goes far beyond a good trademark. If you don't have a good idea and implement well you'll go nowhere fast; good trademark or not.

In short, Yes. But first of all you have to have the idea of what is trademark and complete understanding of that. Check this trademark related articles for professional help. http://www.smallbusinessbible.org/navigation/tm.html

Why may I ask are you concerning yourself with a trademark if you haven't even got an online community? First and foremost a trademark wont really boost the 'wow' factor when they visit your community. I would first suggest build up your community get a good fan base and then possible think about getting a trademark. But keep an eye out for rival communities with the same name.

If you have an amazing name trademark it, but there really isnt much point just for the sake of it, and you need to make sure you get the applications right; so you may end up paying £500 for legal consultancy; Ask yourself are you going to make that money to pay for it? Its not much of an investment I must say; but it could be worth it... Maybe wait until you make enough turnover to afford a trademark or there is a threatr (e.g International Company witht he same name)