Use slot to use custom_icon helper.

app/assets/javascripts/issuable_time_tracker.js.es6

@@ -111,6 +111,7 @@
     template: `
         <div class='time-tracking-component-wrap' v-cloak>
           <div class='sidebar-collapsed-icon'>
+            <slot name='stopwatch'></slot>
             <div class='time-tracking-collapsed-summary'>
               <div class='compare' v-if='showComparison'>
                 <span>{{ abbreviateTime(spentPretty) }} / {{ abbreviateTime(estimatedPretty) }}</span>

app/assets/stylesheets/pages/issuable.scss

@@ -409,6 +409,10 @@
 }
 
 #issuable-time-tracker {
+  > .stopwatch-svg {
+    display: none;
+  }
+
   .time-tracking-help-state {
     padding: 10px 0;
     margin-top: 30px;

app/views/shared/issuable/_sidebar.html.haml

@@ -79,6 +79,8 @@
             .title.hide-collapsed
               Time tracking
               = icon('spinner spin')
+            .stopwatch-svg{ slot:'stopwatch' }
+              = custom_icon('icon_stopwatch')
       - if issuable.has_attribute?(:due_date)
         .block.due_date
           .sidebar-collapsed-icon