The Foyle MLA requested the meeting following concerns about the display of emblems at a parade in Derry last month.
Clyde Valley Flute Band from Larne worn Parachute Regiment insignia and the letter ‘F’ on their shirt during a parade in the city.
Police had to escort them around the outgoing leg of the parade but the band were not allowed to make the return leg.
Said Mr Eastwood: “We have had a positive and useful meeting with the Apprentice Boys on Tuesday evening.
“This city has long led the way in creating the space for mutual accommodation between all communities and traditions.
“I am keen to do whatever I can to maintain the relationships we have built and the progress we have all made.
The Apprentice Boys also recently met with the Bloody Sunday Trust over the parade incident.
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