You don't necessarily need a pump. If you sink your reactor into a body of water, it may use the water as both cooling and the mechanism that powers the turbine. Pumpless cycling of heated fluids is the basis for several non-nuclear thermal energy systems such as OTEC.
To quote MIT on the subject:
“It’s very close to the ocean, which is essentially an infinite heat sink, so it’s possible to do cooling passively, with no intervention. The reactor containment itself is essentially underwater.”
http://news.mit.edu/2014/floating-nuclear-plants-could-ride-...
Using the water as a limitless heatsink is also the cooling mechanism for the currently operational Akademik Lomonosov, which is the world's northernmost nuclear power plant. Russia is currently working on far more of them for its arctic drilling operations, and China is currently working on its first.