The robe and shoulders in this outfit are available from the Moria medallions to the lore classes (minstrel, loremaster, runekeeper). Doing the Moria instances at the 55-60 levels is like doing the Great Barrows at the 20-25 levels. Most of the Moria instances are easy and straight forward, with Grand Stairs being the easiest and fastest way to get your medallions. Still the others are fun too and most classes need to go there for their level 60 class quest anyway. Even if you’re not interested in the gear stats, the class armour still provides some impressive cosmetic looks for most classes. Unfortunately the minstrel class has the ugliest gear of all. The robe in this outfit (purple level 60) is sort of alright, but the shoulders are very very… grey, so that severely limits their use. However, the teal level 60 minstrel gear is really very ugly (with exception of the shoulders). So ugly that I have not found a proper way to use it in an outfit and I probably never will. Since my minstrel still wears 2~4 Moria pieces, I am eternally grateful for the outfit system!
I bought the Elegant Plumed Hat on the cosmetics lotro store sale this week, and thought it was a good match for the robe and shoulders.

Chest: Song-caller’s Robe, red dye (Moria barter, minstrel)

Head: Elegant Plumed Hat, red dye (Lotro store exclusive cosmetic)

Shoulders: Song-caller’s Shoulders, red dye (Moria barter, minstrel)

Hands: Elven Cotton Gloves, grey dye (crafted, light)

Feet: Elven Leather Boots, grey dye (crafted, medium)