Try to take out ling range targets like kinessa. And try to predict the position of fast moving champions.
Be the last one down by timing your heals so that your team can regroup around you even if you die by then
Encountering Grover in long range open spaces - don't PEEK around the corner.
Good Grover players throw axes preemptively and you can take a lot of damage. Use short sprints between cover. This way it's harder to predict where to aim.
Unlike most front liners and supports grover has very good long range pressure. He can use his bonus damage scaling legendary to harass enemy front liners from long range or long range enemies from the objective easily.
Check at the start of the match if Grover has the legendary card which gives him the ability to root with crippling axe, if he does then but the item to reduce CC duration, this can save your life many times during a match.
Grover's ultimate does not make him CC immune but stunning him will not cancel the aoe heal. Displacement heavy comps are very powerful against him since they can keep him away from his team and reduce his healing.