You have to add the NX button to Teamcenter's GUI in order to be able to start NX directly with Teamcenter.
To do so, go to "My Teamcenter", by clicking the respective button on the lower left or by clicking "Home". The bar on the top is missing the NX button (figure "bar without NX button").
To add the NX Button, click Edit -> Options... (figure "Options"). Click NX and check YES right next to Show "Open in NX" Command. Confirm by clicking OK.
The NX Button was added to the menu bar, which should now look like figure "bar with NX button".