Ruby, 41 37 characters

->a{m=a[0];a.map{|n|m>n ?p: m=n}-[p]}

Sample run:

2.1.5 :001 > [
2.1.5 :002 >     [1, 2, 5, 4, 3, 7],
2.1.5 :003 >     [10, -1, 12],
2.1.5 :004 >     [-7, -8, -5, 0, -1, 1],
2.1.5 :005 >     [9, 8, 7, 6, 5],
2.1.5 :006 >     [10, 13, 17, 21],
2.1.5 :007 >     [10, 10, 10, 9, 10],
2.1.5 :008 > ].each{ |test| p ->a{m=a[0];a.map{|n|m>n ?p: m=n}-[p]}[test] }
[1, 2, 5, 7]
[10, 12]
[-7, -5, 0, 1]
[9]
[10, 13, 17, 21]
[10, 10, 10, 10]

Ruby, 32 characters

->a{m,=a;a.select{|n|m<=n&&m=n}}

Thanks to:

• Value Ink for reminding that in Ruby all numbers are truthy, so && number assignment does not change the preceding boolean expression.

Try it online!

Ruby, 41 37 characters

->a{m=a[0];a.map{|n|m>n ?p: m=n}-[p]}

(My old attempt.)

Sample run:

2.1.5 :001 > [
2.1.5 :002 >     [1, 2, 5, 4, 3, 7],
2.1.5 :003 >     [10, -1, 12],
2.1.5 :004 >     [-7, -8, -5, 0, -1, 1],
2.1.5 :005 >     [9, 8, 7, 6, 5],
2.1.5 :006 >     [10, 13, 17, 21],
2.1.5 :007 >     [10, 10, 10, 9, 10],
2.1.5 :008 > ].each{ |test| p ->a{m=a[0];a.map{|n|m>n ?p: m=n}-[p]}[test] }
[1, 2, 5, 7]
[10, 12]
[-7, -5, 0, 1]
[9]
[10, 13, 17, 21]
[10, 10, 10, 10]

Ruby, 41 characters

->a{m=a[0];a.map{|n|m>n ?p: m=n}.compact}

Sample run:

2.1.5 :001 > [
2.1.5 :002 >     [1, 2, 5, 4, 3, 7],
2.1.5 :003 >     [10, -1, 12],
2.1.5 :004 >     [-7, -8, -5, 0, -1, 1],
2.1.5 :005 >     [9, 8, 7, 6, 5],
2.1.5 :006 >     [10, 13, 17, 21],
2.1.5 :007 >     [10, 10, 10, 9, 10],
2.1.5 :008 > ].each{ |test| p ->a{m=a[0];a.map{|n|m>n ?p: m=n}.compact}[test] }
[1, 2, 5, 7]
[10, 12]
[-7, -5, 0, 1]
[9]
[10, 13, 17, 21]
[10, 10, 10, 10]

Ruby, 41 37 characters

->a{m=a[0];a.map{|n|m>n ?p: m=n}-[p]}

Sample run:

2.1.5 :001 > [
2.1.5 :002 >     [1, 2, 5, 4, 3, 7],
2.1.5 :003 >     [10, -1, 12],
2.1.5 :004 >     [-7, -8, -5, 0, -1, 1],
2.1.5 :005 >     [9, 8, 7, 6, 5],
2.1.5 :006 >     [10, 13, 17, 21],
2.1.5 :007 >     [10, 10, 10, 9, 10],
2.1.5 :008 > ].each{ |test| p ->a{m=a[0];a.map{|n|m>n ?p: m=n}-[p]}[test] }
[1, 2, 5, 7]
[10, 12]
[-7, -5, 0, 1]
[9]
[10, 13, 17, 21]
[10, 10, 10, 10]