增 (zēng) is a formal, written bound form meaning 'to increase, augment' — it almost always combines with another character (增加, 增强, 增长). 提高 (tígāo) means 'to raise/improve' and often implies a level or quality; 增加 (zēngjiā) is the common, standalone verb for 'to increase' in number or amount. 增 is more literary and rarely used alone.