1
diligent application (to work or study);cultivating one's character by studying hard
君の実力なら楽勝だとは思うが、それに驕らず、まずはクラスのみんなと切磋琢磨していって欲しい。
I think you could easily win with your ability, but I want you to not be arrogant about it and work hard with everyone in your class first.
2
mutual encouragement (to improve);working hard together;friendly rivalry
Other forms
切瑳琢磨 【せっさたくま】 (rarely used kanji form)