Mr Gillies is to stay in the remuneration post at the Edinburgh pensions and investment house until its annual meeting on May 13, where he hopes to secure investor approval for a new bonus arrangement thrashed out with major shareholders.
Ms Peacock, who has been on the Standard Life board since 2012, will receive a £25,500 rise in fees in her expanded part-time position. Non-executive directors receive a basic £71,400 fee with extra allowances for additional duties.
She is no stranger to controversy over pay, having received a £475,000 termination payment as part of a £1.5 million package for her final nine months at Glasgow-based Clydesdale in 2010.
Since her departure Clydesdale has undergone an extensive restructuring and handed a book of toxic property loans to its parent National Australia Bank.
One of the most senior people in British banking, Ms Peacock was at Clydesdale for eight years having previously run Woolwich.
She is currently also a non-executive director of Scottish Water and of Nationwide Building Society.
Mr Gillies will take a seat on the Barclays board from May 1, although a date has not yet been confirmed for him to assume chairmanship of the remuneration committee.
On top of an £80,000 fee for being a director, he will get an additional £70,000 a year for chairing the pay committee.
His appointment will be seen as an emollient move ahead of a potential shareholder revolt at next week's annual general meeting following a year in which it paid out nearly £2.4 billion in bonuses.
Mr Gillies, the current chairman of Scottish Enterprise, will replace Sir John Sunderland as chairman of its remuneration committee.
He had a career as a management consultant, rising to be managing director of Bain & Company.
The Scots-born former Perth Academy pupil is a former chairman of the Confederation of British Industry. He also sat on the management board of the Department of Trade & Industry between 2002 and 2007.
He has been on the Standard Life board since 2007.
Barclays chairman Sir David Walker said: "He brings immense experience in a range of different industries, including the financial services sector, in addition to a background in strategy and the public sector."
The switch comes amid anger over Barclays' decision to increase the bonus pool by 10% last year, despite a 32% fall in underlying profits.
Shareholder lobby group Pirc last week recommended that investors oppose five resolutions at next Thursday's annual meeting in London, including the remuneration report and reappointment of Sir John.
Chief executive Antony Jenkins said recently that the pay and bonus awards were necessary in order to retain top talent in its investment banking arm.
Pirc is also unhappy that Mr Jenkins will get up to £1m in share allowances on top of salary and bonuses to defy new European rules to cap payouts.
Sir John, who spent 40 years with Cadbury Schweppes, has been on the Barclays board since 2005.
Earlier this month, Standard Life wrote to shareholders asking them to back a new pay plan to give the board greater powers to strip executives of awards if future performance shows they didn't deserve them but which also permits long-term incentive awards of up to 300% of salary.