To 'sing up' means increasing volume so more people can hear you without yelling or screaming. The coach told the players to 'sing up' so everyone on the field could hear the chant.
Pro Tip 2/3
Clarity Counts
'Sing up' also suggests pronouncing words clearly, not just loudly, when singing. The director said 'sing up' because the lyrics were unclear to the audience.
Pro Tip 3/3
Not for Speech
The phrase 'sing up' is specific to singing and doesn't apply to normal speaking situations. During rehearsal, the soloist was told to 'sing up,' not to speak louder.