In light of the recent announcement that the Duke and Duchess of Sussex (aka Prince Harry & Meghan) will be stepping back from duties as senior royals and, consequently no longer styling themselves as “royal highness” not a few people have contacted me to ask out of curiosity if this in any way will have an impact on the coats of arms they both use.
The simple answer is, “No”.
As the grandson of the sovereign Prince Harry employs a coat of arms that indicates he was born a grandson of the sovereign. British royal heraldry is different than many other countries in that the sovereigns children and grandchildren generally bear the royal arms differenced by a variety of labels of either three or five points and the points are charged with marks of difference. That’s really rather boring if you asked me but that’s what they do and they haven’t asked me!
So, when he turned 18 Harry was granted his own arms depicting the royal arms difference by a label of five points the first, third and fifth of which are charged with a red escallop shell. The shell is a charge borrowed from the coat of arms of his late mother, Diana (neé Spencer).
His supporters were also charged with the label for difference and the arms are surmounted by a special coronet used by the children of the heir to the throne. In addition, the royal crest is also charged with the label for difference.
Upon marrying his wife Harry was created Duke of Sussex. Nothing in his coat of arms was modified to reflect this title. Consequently, there is nothing to change in his coat of arms to reflect his new status of stepping down from a senior position in the royal family. He is still a grandson of the sovereign and son of the heir to the throne; he is still the Duke of Sussex; he is still actually an “HRH” but will choose not to style himself as such.
In fact, even after his grandmother passes away and he is the son of the sovereign and, indeed, even after his father passes away and he is the brother of the sovereign the crown used on his arms will remain unchanged as the crown for the child of the heir is identical to the crown used by children of the sovereign and siblings of the sovereign.
So…no changes.
EXARANDORUM 
Whilst the crown adorning his shield will not change on his grandmother’s death the label on shield, supporters and crest will change subtly: the two plain points will disappear. That was confirmed some years ago by Garter Gwynne-Jones.
Yes, I was careful not to say that his entire achievement would not change after the deaths of his grandmother or father but commented only on his coronet.