draw ‧ bridge /ˈdrɔːbrɪdʒ $ ˈdrɒː-/ BrE AmE noun [countable]
1 . a bridge that can be pulled up to stop people from entering a castle, or to let ships pass
2 . pull up the drawbridge
a) to stop being involved in something:
Perhaps we should just pull up the drawbridge and let them get on with it.
b) to stop more people coming into a country, joining an organization etc