I was wondering if there exists a book/work that was written exclusively as a perush on the beur HaGra whether it be on only a chelek of the Shulchan Aruch or otherwise?
The difficulty of the Biur ha-Gra as an impediment to its study was noted immediately with its publication. In the introduction to his Taklin Chadatin (Minsk, 1812), R. Yisrael of Shklov already noted the necessity for a commentary on the Biur ha-Gra: "לזה צריך חיבור בפני עצמו יותר ויותר מחיבור הפרי מגדים על המגינים". But this need has gone largely unfulfilled until the last few decades and still remains incomplete. In the first such commentary, R. Eliezer Landau’s Damesek Eliezer (Vilna, 1868) on the Biur ha-Gra on Orach Chayyim, the author explains that the purpose of his work is to increase the study of the Biur ha-Gra, which “until now is like a sealed book, which almost no one seeks”: אך חפצי כי יתרבו הלומדים ביאורי הגר"א אשר עד כה הוא כספר החתום, כמעט אין דורש אותו. R. Abraham Isaac Kook, who saw the Gra as a model for his project of unifying the halakhah with its sources, also recognized that the Biur ha-Gra was hardly used because of its terseness: "כבר אמרתי שהשימוש בביאורי הגר״א בחוג הלומדים הוא כ״כ ממועט מפני קיצורו הגדול" (Hartza’at ha-Rav, Jerusalem, 1920, p. 14). His own commentary, Be’er Eliyahu (first published in Sefer ha-Gra, Jerusalem 1954), covers only the Biur ha-Gra on the first section of Choshen Mishpat. The commentary Birkat Eliyahu, which R. Barukh Rakover began publishing in 1968 under R. Kook’s inspiration, now contains twenty seven volumes, but is still missing the entire Yoreh De’ah section of Shulchan Arukh. The four-volume work שלמת אליהו is a commentary on parts of Yoreh De'ah, but also remains incomplete.
--Birkas Eliyahu (ברכת אליהו) is a multi-volume work on Biur HaGra which is available for free on hebrewbooks.org
--there is also damesek eliezer דמשק אליעזר which is a commentary to the biur hagra.
-- there is also a commentary to biur hagra written by a Rosh Kollel in Landers College, but I don't remember his name or the name of his sefer.
Yes. Bircas Eliahu by Baruch Rokover, printed by Mosad HaRav Kook. ברכת אליהו
It can also be found on the אוצר החכמה, if you are registered.
Also נר חיים by Rabbi Lipshutz on most of יורה דעה ח"א נר חיים was authentic by Rabbi Chaim Kirschenbaum on הלכות מליחה תולעים בשר בחלב תערובות All volumes except for תערובות are still in print