Clear Search History

Welcome to the forum. I want to make certain you are talking about Chrome, the browser and not the stock browser.They are not the same. If it is Chrome there is no way to clear just the history. You would need to go to the app manager > all and find chrome to clear out, (think) both cache and data.
Bring up the browser.
Tap the three vertical dots in the upper right hand corner.
Tap "History".
Scroll to the end of the history.
Tap "Clear Browsing Data" on the last line.
Check the box for "Clear Browsing History". (And whatever else you want to clear.)
Tap "Clear".

BTW Chrome is the default browser on the N7 2013.