Samuel West in RSC’s Richard II, part of the This England: The Histories series (2000)

Does Jonathan Groff know his Shakespeare from his Sondheim?

(Spoiler: 100%, yes he does)

About Rhaegar -

Some believe the entire tourney had in fact been organised by Rhaegar to gather the great lords of Westeros and address the madness of his father Aerys, perhaps even to remove him from the Iron Throne. Very much Edward the Black Prince energy.

The Edward the Black Prince comparison is interesting considering all this from wiki -

He was regarded by English contemporaries as a model of chivalry and one of the greatest knights of his era.[2] Edward married his half-first cousin once removed Joan, Countess of Kent, in early 1361. Their wedding was conducted in secret, and was later annulled the same year because of lack of needed dispensation, but afterwards the couple managed to obtain the necessary documents and married once again on 10 October 1361.

Rickard Stark -

His three children are with him, and he is in the midst of carefully arranging their futures – Brandon’s betrothal to Catelyn Tully, and Lyanna’s to Robert Baratheon.

Lyanna Stark -

present with her family, betrothed to the Lord of Storm’s End Robert Baratheon. Headstrong, wise, capable at arms and never one to shy away from a fight, Lyanna’s life is completely about to change.

Eddard Stark -

18 years old and fresh from his fostering at the Eyrie under Jon Arryn alongside Robert. He is betrothed to no one at this point, but will notice Ashara Dayne at the opening feast, and she will notice him.

Tywin Lannister -

His relationship with the king is close to breaking point, and about to be blown apart by Aerys’ decisions at Harrenhal.

Cersei Lannister -

She is not yet married and is being quietly positioned to be betrothed by Tywin somewhere very advantageous.

Elia Martell -

pregnant again (with Aegon, who will be born shortly after). Her health is fragile. She is here in the place of honour, presumably to be showered with love by her husband.

Ser Oswell Whent -

Attending as Kingsguard, and notably it was his visit to his brother Lord Whent that is widely understood to have been the prompt for the tournament being announced.

Ashara Dayne

attending as a lady-in-waiting and one of the great beauties of the realm. She dances at the opening feast and catches more than one eye: including, reportedly, Ned Stark’s.

Catelyn Tully -

Not actually at Harrenhal. She is back in Riverrun at the start of the story, betrothed to Brandon Stark but not yet his wife. She has likely never met Ned Stark.

Howland Reed -

He will become one of the most important witnesses to everything that follows.

Lord Varys

According to current writing he is not at Harrenhal in person, but his intelligence is everywhere.

Lord Owen Merryweather and Qarlton Chelsted who are involved in the politics between Rhaegar and Aerys -

An amiable but ultimately ineffectual man, his significance unexpectedly grows as the tragic tale progresses.